If cos(x) + sin(x) = √2cos(x), what is the value of cos(x) - sin(x)?
Q1. If cos(x) + sin(x) = √2cos(x), what is the value of cos(x) - sin(x)?
Answer: √2sin(x)
Explanation: Squaring both equations and adding them gives 2 = 2cos²(x) + 2sin²(x) - 2sin(x)cos(x) + 2sin(x)cos(x), which simplifies to an identity, then using the given equation, we can derive cos(x) - sin(x) = √2sin(x).